Order alpha_s^2 magnetic penguin correction for B decay to light mesons

Abstract

We compute the order alpha_s^2 correction to the matrix element of magnetic penguin operator for B meson decaying to light mesons within the QCD factorization framework. We explicitly show that the soft and collinear divergences are canceled out, so that the validity of QCD factorization is confirmed. We present the result of the calculation in complete analytic forms. The result is also applied to B -> K pi decays, and we find that the order alpha_s^2 correction of magnetic penguin operator can considerably reduce the coefficient of penguin amplitude a^c_{4,I}. The reduction is stronger for the imaginary part.